Page 105 - Maths Skill - 6

Perimeter and Area 103

4. One side of the square figure is 30 cm. Find its perimeter.
5. The perimeter of square is 36 m. Find the side of this square.
6. Find the cost of fencing a square field of side 24 m at the rate of ` 10 per m.

7. Find out the side of square whose perimeter is 40 cm.
8. Find the perimeter of a regular hexagon with side 6.5 cm.
9. Find the side of a regular octagon whose perimeter is 96 cm.
10. A wire is bent to form a rectangle of 28 m × 10 m. It is again straightened and bent now to form a
square. What is the side of the square so formed?

AREA
Region enclosed by a closed figure is called its area.

The shaded portion of the Fig. aside shows the
surfaces enclosed by them i.e., area of the figure.

Units of Length and Area
Let’s review the standard measures of length and area.

Measure of length Measures of area Fact-o-meter
1 cm = 10 mm 1 cm 2 = 100 mm 2

1 m = 100 cm 1 m 2 = 10000 cm 2 � Units of area used for the
measurement of land, field,
1 dm = 10 cm 1 dm 2 = 100 cm 2 etc. are:
1 dam = 10 m 1 dam 2 = 100 m 2 1 are = 100 m 2

1 km = 10 hm 1 km 2 = 100 hm 2 1 hectare = 10000 m 2
1 km = 1000 m 1 km 2 = 1000000 m 2

AREA OF A RECTANGLE

In a rectangle the larger side is called its length and the smaller side is called its breadth.
Let us do an activity to derive a formula to calculate the area of a rectangle.

Activity
Draw a rectangle ABCD on a graph paper such that length (AB) = 6 cm
and breadth (BC) = 3 cm. We know that, the area of each square region A 3 3 3 3 3 3 B
2
(3 marked) is 1 cm as shown in the given figure. 3 3 3 3 3 3
Count the number of such squares (3 marked) contained in this 3 3 3 3 3 3
rectangle. D C
Clearly, there are 18 squares.

∴ Area of rectangle = 18 cm 2 ...... (i)
2
Also, if we multiply length and breadth, we get length × breadth = 6 cm × 3 cm = 18 cm ...... (ii)
Thus, from (i) and (ii), we get

Area of a rectangle = (length × breadth) square units.
From the above relation, we can also find the value of length or breadth.
Area Area
(i) Length = Breadth units (ii) Breadth = Length units